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Homework Help: Find the ratio of the frequency of the damped oscillator

  1. Oct 1, 2007 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

    2. Relevant equations
    [tex]T=\frac{ 2\pi}{w_1}[/tex]

    [tex] w_1^2=w_0^2- {\Beta}^2[/tex]

    3. The attempt at a solution
    I know the answer is [tex]\frac{w_1}{w_0}=\frac{8 {\pi}}{\sqrt{64 {\pi}^2+1}}[/tex]

    However, I think I am missing an equation here because using only the two above i cannot obtain this answer. If someone could point me in the right direction I would appreciate it!

    Last edited: Oct 1, 2007
  2. jcsd
  3. Oct 1, 2007 #2


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    Staff Emeritus
    Science Advisor

    Well, firstly you should explain your symbols. I presume you are using w to mean omega; the frequency of the oscillator. What is the definition of the natural frequency?
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